First, let me state that the FNIRSI HRM-10 is an excellent piece of test equipment. The voltage and resistance values are super precise and super accurate.
The purpose of such a "AC" tool is to evaluate the quality of new batteries coming down the assembly line. If the electrolyte is poor (voltage out of range), or the metal attachments of wires are poor (internal resistance out of range), this meter will be able to reject those conditions. It does so by comparing the test result to the established limits which can be input by the user. If the reading is out of range, the part or lot of parts are flagged.
The HRM-10 will report the open circuit voltage and the internal resistance of the cell. It DOES NOT PLACE A LOAD on the cell. The equivalent in a vehicle is measuring the torque of the engine and checking the slop in the drivetrain, but not actually applying horsepower to the wheels and driving it around.
Next, I must tell you that the readings of this unit are not very good at evaluating the state of health of the cells. Meaning, as your cell ages, other ways of testing will produce more meaningful results. You need a tester that "puts the cell on the dyno". One such tester is the Opus BT-3400. It will fully cycle a rechargeable cell, and also features a "quick test" which measures DC resistance UNDER LOAD. Both these two values (mAh and mR) can be used to compare the new result to the result when the cell was new. If you weren't tracking your rechargeable cell from new, you can instead compare your result to the exact product datasheet.
Your questions lead me to believe you are testing rechargeables, so look to Opus or Maha for appropriate devices that include the types of cells you want to test.
To answer your question about charging, the Opus manual recommends testing a fully charged cell, since it places a temporary DC load on the cell and measures how much the voltage drops. A partially or fully discharged cell would provide skewed results. If you are using the FNIRSI, I don't think it matters much the state of charge. The AC impedance results should be similar either way. I personally use a fully charged cell. I don’t think comparing internal resistance for different states of charge is meaningful.
If you happen to be testing primaries (not rechargeable) I would change my recommended tool. First method is with a regular voltmeter and resistor, or using just a meter with an appropriate battery test function. Do an open circuit voltage test first, note the value. Then apply a load which is 1/10 of the mA*h rating of the cell (for instance 15 mA for a 150 mA*h 9V rectangle cell). Observe how much the voltage reading changes. If it goes from 9.5V to 8.5V, the cell is probably like new. If it goes from 8.5V to 6.5V, the cell is nearly expired.
If you want to do a full discharge of a primary cell, which is of course destructive, you'll want a tool that reports mW*h or W*h. The "W" signifies is power, similar to horsepower in a car. You want to avoid "mA*h" or "A*h" test, which is similar to measuring RPM of an engine. Unfortunately, common tools designed for rechargeable cells are being misused by YouTubers to evaluate primary cells and they wonder why they get strange results. The best assessment of the quality of a primary cell is to measure the total power the cell can provide. Power in Watts is Volts times Amperes, not Amperes alone. Very important for accurate assessments! Comparing mAh measurements across different cell chemistries contains a great deal of error. Comparing across different brands of the same chemistry also will carry some error, but not as much as comparing lithium to alkaline and so on.
The HRM-10 can be used to measure the open circuit voltage. With experience, this can be useful for determining the POSSIBLE capacity remaining in a cell. Then again, any volt meter can do this. The internal resistance check will only tell you whether or not the cell is made to high quality standards. The lower the internal resistance, the better it is constructed. If you get a zero voltage reading and a zero resistance reading, the cell is shorted.
Hopefully nobody is buying this unit thinking they can check the state of health of their batteries around the house and in their cars. It can't really do that, other tools are much better. However, if you are building battery packs from raw cells, this device can help match up similar quality cells so that they discharge at the same rate. The device can also identify bad cells in a poorly performing battery pack. The cell with low voltage and/or high resistance is likely to problem cell.